Euler Number
An introduction and definition of the Euler Number in fluid mechanics
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The Euler Number is a dimensionless value common used for analyzing fluid flow dynamics problems where the pressure difference between two point is an important variable. The Euler Number can be interpreted as a measure of the ratio of pressure forces to inertial forces.
The Euler Number can be expressed as
Eu = p / (ρ v2) (1)
where
Eu = Euler number
p = pressure (Pa)
ρ = density (kg/m3)
v = fluid flow velocity (m/s)
The pressure difference as shown below is often used
Eu = dp / (ρ v2) (2)
where
dp = differential pressure (Pa)
The combination below is called the pressure coefficient
pressure coefficient = dp / (1/2 ρ v2) (3)
A special version of the Euler Number is in general referred to as the Cavitation Number.
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